Trigonometry Examples

\tan (2.5) (18 + x) = \tan (10) x

$\tan (2.5) (18 + x) = \tan (10) x$

Step 1

For the two functions to be equal, the arguments of each must be equal.

2.5 = 10

$2.5 = 10$

Step 2

Since

2.5 \neq 10

$2.5 \neq 10$ , there are no solutions.

No solution

Step 3

The tangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from

π

$π$ to find the solution in the fourth quadrant.

2.5 = π + 10

$2.5 = π + 10$

Step 4

Subtract

2 π

$2 π$ from

π + 10

$π + 10$ .

2.5 = π + 10 - 2 π

$2.5 = π + 10 - 2 π$

Step 5

The resulting angle of

10 - π

$10 - π$ is positive, less than

2 π

$2 π$ , and coterminal with

π + 10

$π + 10$ .

2.5 = 10 - π

$2.5 = 10 - π$

Step 6

Subtract

2 π

$2 π$ from

10 - π

$10 - π$ .

2.5 = 10 - π - 2 π

$2.5 = 10 - π - 2 π$

Step 7

The resulting angle of

10 - 3 π

$10 - 3 π$ is positive, less than

2 π

$2 π$ , and coterminal with

π + 10

$π + 10$ .

2.5 = 10 - 3 π

$2.5 = 10 - 3 π$

Step 8

Solve for

x

$x$ .

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Step 8.1

Simplify

10 - 3 \cdot 3.14159265

$10 - 3 \cdot 3.14159265$ .

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Step 8.1.1

Multiply

- 3

$- 3$ by

3.14159265

$3.14159265$ .

2.5 = 10 - 9.42477796

$2.5 = 10 - 9.42477796$

Step 8.1.2

Subtract

9.42477796

$9.42477796$ from

10

$10$ .

2.5 = 0.57522203

$2.5 = 0.57522203$

2.5 = 0.57522203

$2.5 = 0.57522203$

Step 8.2

Since

2.5 \neq 0.57522203

$2.5 \neq 0.57522203$ , there are no solutions.

No solution